Emergent long-tail dynamics in driven magnets with dynamical frustration

Abstract

In this study, we show that dynamical frustration can spontaneously emerge in frustration-free magnetic systems under periodic driving. Specifically, we consider a classical spin system and demonstrate the emergence of spin-ice physics when drive-induced heating is well suppressed. In particular, we focus on the dynamics of magnetic monopole excitations, which, in sharp contrast to their equilibrium counterparts, exhibit a non-ergodic stochastic random-walk process with long-tailed, power-law distributed waiting times, where the power-law exponent is tunable by the system's effective temperature. Heating is accelerated at intermediate driving frequencies, and the system eventually heats up to an infinite-temperature state. However, the heating time is extremely sensitive to different initial-state realizations and also follows a long-tailed power-law distribution. We show that a drive-induced short-range attractive interaction between monopoles is responsible for the long-tailed distributions observed in both monopole and heating dynamics.

Figures (3)

• Figure 1: (a)Sketch of the ternary driving protocol within one period and the instantaneous ground state of $H(t)$. The green(blue) solid bonds indicate the AF coupling between the NN (NNN) spins. (b)Sketch of the effective Floquet Hamiltonian in fast driven case. The initial state is prepared as a SI state with a spin flip (red arrow), which generates a pair of monopoles in adjacent plaquettes (pink $\boxtimes$).
• Figure 2: (Color online)(a)Dynamics of the stroboscopic energy per site $\varepsilon_n$ and the spin ice parameter $D_n$ in different trajectories starting from initial states with various noise realizations in fast driven case. (b)The dynamics of the total number of flipped spins $\delta S_z$ during the movement of monopoles in a single trajectory. The inset shows the position of two monopoles at the time slices within a plateau (green) and between two plateaus (red). (c)$P(\tau)$ with a fixed $T=0.3J^{-1}$ but various $W$ (upper panel) and a fixed $W=0.2J$ but various $T$ (lower panel). The statistics are performed over $\mathcal{N}=500$ trajectories. The inset shows the noise strength $W$ dependence of $\eta$. The driving period is chosen as $T=0.3J^{-1}$ for (a) and (b). The system size is $L=20$.
• Figure 3: (a)Dynamics of $\varepsilon_n$ in different trajectories starting from initial states with various noise realizations in the presence of intermediate driving. (b)The cumulative distribution function of the prethermal plateau duration $P(\tau_0)$, which also exhibits a power-law decay for large $\tau_0$ (log-log plot). (c)$P(\tau_0)$ for small systems (semi-log plot), which exhibit an exponential decay for large $\tau_0$: $e^{-\tau_0/\gamma}$. The statistics are performed over $\mathcal{N}=2\times10^4$ trajectories. The inset shows the size dependence of $\gamma$. The parameters are chosen as $L=20$, $T=5.2J^{-1}$, $W=0.1J$ for (a)-(c).